Matlab的分数阶控制系统仿真研究
关键词 分数阶微积分 整数阶PID控制器 分数阶 控制器8220
毕业设计说明书（论文）外文摘要
Title ：Matlab based on the fractional order system simulation research
Abstract
As many complex systems are fractional in mordern industry, traditional integer order PID controller can not be very good control.Based on this problem, scholars have proposed fractional order controller. This paper firstly introduced the difinition character transform of Laplace transform of Fourier of fractional order calculus, Differential equation and its solution; Secondly, introduced the fractional control system, fractional order controller;Again, studied the performance comparison between integer order PID controller and fractional order controller.;Finally, introduced the impacts on the performance of fractional order closed loop system caused by the five parameters in fractional order controller. The simulation results show that when we control fractional order control system with fractional order controller. Its control performance is better than that with integer order PID controller,its response time is faster,the overshoot is smaller,the number of shocks reduces;the effects of ， ， are nearly the same with the three parameters of integral PID controller ;μ mainly affects the overshoot, λ influences system accuracy.
Keywords: fractional order calculus integer order PID controller fractional order controller
目 录
1 绪论1
1.1 研究背景1
1.2 研究现状2
1.3 分数阶系统中应用的关键技术2
1.4 本文研究的内容3
2 分数阶微积分3
2.1 分数阶微积分的定义3
2.2 分数阶微积分的性质6
2.3 分数阶微积分的Laplace变换6
2.4 分数阶微积分的Fourier变换8
2.5分数阶微分方程的数值解法13
3.分数阶控制系统概述17
3.1 分数阶控制系统概述18
4 分数阶 控制器的设计以及与整数阶PID控制器的控制性能比较24
4.1 主导极点法25
4.2 整数阶PID控制器设计和分数阶 控制器的控制性能比较29
5 分数阶 控制器参数变化对闭环系统性能的影响34
5.1 值的变化对系统性能的影响37
5.2 值的变化对系统性能的影响40
5.3 值的变化对系统性能的影响42
5.4 值的变化对系统性能的影响43
5.5 值的变化对系统性能的影响45
5.6参数变化对系统性能的影响总结47
6总结与展望48
6.1内容总结48
6.2研究展望49
致谢 50
参考文献 51
1. 绪论
分数阶微积分（Fractional Derivatives and Iniegals，或Fractional Calculus, 简写为FC）。即指函数对变量非整数阶求导或积分，是古典微积分理论的自然推广，为数学分析的一个分支。分数阶微积分理论建立至今已经有300年的历史了，它把传统整数阶导数的阶次推广到分数甚至复数领域，极大地拓展了传统导数的概念。自从分数阶微积分出现以来，就引起了许多著名科学家的兴趣，其中有著名的傅里叶(Fourier)，欧拉(Euler)，拉普拉斯(Laplace)等。
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